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A242180 Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009. 1
1, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 19, 23, 1, 1, 1, 89, 13, 61, 71, 1, 1, 37, 1, 1, 17, 1, 7, 1, 1, 167, 1, 1, 491, 53, 1, 31, 1, 227, 1, 1, 1, 97, 1, 59, 241, 29, 1, 953, 1063, 1777, 1, 367, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Conjecture: a(n) > 1 for all n > 203.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..6000

EXAMPLE

a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5).

a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2.

MATHEMATICA

f[n_]:=FactorInteger[PartitionsQ[n]]

pp[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]

Do[If[PartitionsQ[n]<2, Goto[cc]]; Do[Do[If[Mod[PartitionsQ[i], Part[pp[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[pp[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[pp[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 60}]

CROSSREFS

Cf. A000009, A000040, A194261, A272169, A272170, A272171, A272173.

Sequence in context: A110977 A295785 A069230 * A163961 A101387 A117365

Adjacent sequences:  A242177 A242178 A242179 * A242181 A242182 A242183

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, May 06 2014

STATUS

approved

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Last modified May 28 01:34 EDT 2020. Contains 334671 sequences. (Running on oeis4.)